We review the well known microscopic correspondence between random zeros of the Riemann zeta-function and the eigenvalues of a
random unitary or Hermitian matrix, and discuss evidence that this correspondence extends to larger mesoscopic collections of zeros or
eigenvalues. In addition, we discuss interesting phenomena that appears in the statistics of even larger macroscopic collections of
zeros. The terms microscopic, mesoscopic, and macroscopic are from random matrix theory and will be defined in the talk.

This talk is based in part on results in the papers arXiv: 1203.3275 math.NT, and arXiv: 1205.0303 math.PR.